Horizontal Line Test

The horizontal line test is a convenient method that can determine whether a given function has an inverse, but more importantly to find out if the inverse is also a function.

Remember that it is very possible that a function may have an inverse but at the same time, the inverse is not a function because it doesn’t pass the vertical line test.

So these are the rules:

If the horizontal line intersects the graph of a function in all places at exactly one point, then the given function should have an inverse that is also a function. We say this function passes the horizontal line test.

Here are some examples of functions that pass the horizontal line test:

Horizontal Line Cutting or Hitting the Graph at Exactly One Point

Graph of the line f (x) = –x+2

Graph of the square root function

Graph of the rational function

On the other hand, if the horizontal line can intersect the graph of a function in some places at more than one point, then the function involved can’t have an inverse that is also a function. We say this function fails the horizontal line test.

Here are some examples of functions that fail the horizontal line test: